I would guess that this expensive looking piece of probably custom made glassware is used with some highly reactive chemicals where you wouldn't want to open it up to the atmosphere to add reagents. I could imagine a reflux condenser in the middle. The surrounding ports would each serve a specific purpose.

So - Here's an imaginary setup: You fill the main chamber with a solvent and maybe some boiling beads and a stir bar. One or more of the ports could be rigged up to include a thermometer or other probe. A sampling probe might be handy, for example. You'd start it up and add one or two liquid reagents via addition funnels connected to other ports. Let it run for however long, then either add the quenching agent or additional reagents.

This suggests that this is a well established (if small scale) process because there'd be no intermediate purification step.

Two and three necked versions of these are pretty common. This vessel is batshit, though. This also leads me to an alternate theory. Similar to one proposal for the roman dodecahedrons, this could be a glassblower's master thesis.